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arXiv · 1801.02228

On cubic Thue equations and the common index divisors of cyclic cubic fields

Mohammed Seddik
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Abstract

In this paper, we investigate the common index divisors of cyclic cubic fields. Let $a,b,c,d$ and $k$ are integers, we then solve the following Thue cubic equations:: \[ax^3+bx^2y+cxy^2+dy^3= k\ \] when $a,bc+d$ are odd and $3$ doesn't divide $v_2(k)$.

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Mohammed Seddik. 2018-01-07. On cubic Thue equations and the common index divisors of cyclic cubic fields. https://arxiv.org/abs/1801.02228

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